Can't Airplay my MacBook in 16:10 full screen with Apple TV - why not???

I'm trying to Airplay my 13" MacBook Air (16:10 aspect ratio) using my Apple TV HD (can be set to 16:10) connected to an Epson Projector (16:10). But no matter what combination of settings I try, the darn image won't fill the entire 16:10 projected/lit screen. My projector's native resolution is 1280x800.

(1) If the Apple TV is set to 1080p resolution and the MacBook scaled to 1280x800, the projected image is 16:10 but letterboxed all around.

(2) If the Apple TV is set to 1280x800 resolution and the MacBook scaled to 1280x800, the projected image is some odd aspect ratio, letterboxed slightly on the sides and cut off at the top and bottom.

(3) If the Apple TV is set to 1280x800 resolution and the MacBook is set to "Optimize for Apple TV", the projected image is 16:10 but cut off all around. I tried turning the "Underscan" setting on the Apple TV to "on" but it makes no difference.

(4) If I connect the MacBook directly to the projector using an HDMI cable and HDMI to Thunderbolt adapter and scale the MacBook to 1280x800, the projected image is PERFECT (16:10 full screen). So why the heck can't I get that same image with AirPlay???

See images below that show what I describe above:

(1) Apple TV 1080p / MacBook 1280x800 = 16:10 letterboxed all around

(2) Apple TV 1280x800 / MacBook 1280x800 = odd aspect ratio letterboxed on sides and cut off at top and bottom

(3) Apple TV 1280x800 / MacBook "optimized for Apple TV" = 16:10 cut off all around

(4) Direct MacBook to Projector connection via HDMI = 16:10 full screen (this is what I want!)